At the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24
<h3>What is appreciation and deprecation?</h3>
Deprecation, also called devaluation, is the decrement in price of an asset. Appreciation is opposite of deprecation. This indicates increment in the price of the considered thing.
<h3>How to find the percentage from the total value?</h3>
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
![\dfrac{a}{100} \times b](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%7D%7B100%7D%20%5Ctimes%20b)
It is given that:
- Initial price of the plot of land = $350,000
- First year: 12% appreciation
- Second year: 10% appreciation
- Third year: 8% devaluation
- Fourth year: 6% appreciation
Now, consider appreciation of an amount A by P%.
Then, we have:
Increased price = Initial price + P% of initial price
Increased price = ![A + \dfrac{A}{100} \times P = A \times \left(1 + \dfrac{P}{100} \right)](https://tex.z-dn.net/?f=A%20%2B%20%5Cdfrac%7BA%7D%7B100%7D%20%5Ctimes%20P%20%3D%20A%20%5Ctimes%20%5Cleft%281%20%2B%20%5Cdfrac%7BP%7D%7B100%7D%20%5Cright%29)
Similarly, depreciated price by P% of an amount A is:
Decreased price = ![A - \dfrac{A}{100} \times P = A \times \left(1 - \dfrac{P}{100} \right)](https://tex.z-dn.net/?f=A%20-%20%5Cdfrac%7BA%7D%7B100%7D%20%5Ctimes%20P%20%3D%20A%20%5Ctimes%20%5Cleft%281%20-%20%5Cdfrac%7BP%7D%7B100%7D%20%5Cright%29)
We've got: A = 350,000
After 1st year, which had 12% appreciation, we get:
![A_1 =A(1 + 12/100) = A(1.12)\\](https://tex.z-dn.net/?f=A_1%20%3DA%281%20%2B%2012%2F100%29%20%3D%20A%281.12%29%5C%5C)
After 2nd year, 10% appreciation we get:
![A_2 =A_1(1 + 10/100) = A_1(1.1) = A(1.12)(1.1)\\](https://tex.z-dn.net/?f=A_2%20%3DA_1%281%20%2B%2010%2F100%29%20%3D%20A_1%281.1%29%20%3D%20A%281.12%29%281.1%29%5C%5C)
After 3rd year, which had 8% devaluation effect on the price, we get:
![A_3 = A_2(1 - 8/100) = A_2(1-0.08) = A_2(0.92) = A(1.12)(1.1)(0.92)](https://tex.z-dn.net/?f=A_3%20%3D%20A_2%281%20-%208%2F100%29%20%3D%20A_2%281-0.08%29%20%3D%20A_2%280.92%29%20%3D%20A%281.12%29%281.1%29%280.92%29)
After 4th year, which had 6% appreciation effect on the price, we get:![A_4 = A_3(1 + 6/100) = A_4(1+0.06) = A_3(1.06) = A(1.12)(1.1)(0.92)(1.06)](https://tex.z-dn.net/?f=A_4%20%3D%20A_3%281%20%2B%206%2F100%29%20%3D%20A_4%281%2B0.06%29%20%3D%20A_3%281.06%29%20%3D%20A%281.12%29%281.1%29%280.92%29%281.06%29)
Thus, the final effect on A is:
![A \rightarrow A(1.12)(1.1)(0.92)(1.06) = A(1.2014464)\\\$350,000 \rightarrow 350000(1.2014464) = 420506.24\: \rm dollars](https://tex.z-dn.net/?f=A%20%5Crightarrow%20A%281.12%29%281.1%29%280.92%29%281.06%29%20%3D%20A%281.2014464%29%5C%5C%5C%24350%2C000%20%5Crightarrow%20350000%281.2014464%29%20%3D%20420506.24%5C%3A%20%5Crm%20dollars)
Thus, at the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24
Learn more about percent here:
brainly.com/question/11549320
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